Seshadri constants provide a fundamental numerical measure of the local positivity of line bundles. In this talk, I will discuss their interpretation via blow-ups, jet separation, and asymptotic multiplier ideals, highlighting how these invariants encode the geometry of base loci. Finally, I will present examples on surfaces and on blow-ups of \mathbb{P}^2 that illustrate how these ideas appear in explicit calculations and connect to conjectures such as Nagata’s.